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arXiv:0802.1592 · Physical Review A

Quantum pattern recognition with liquid-state nuclear magnetic resonance

Rodion Neigovzen, Jorge Luiz Neves, Rudolf Sollacher, Steffen J. Glaser

Published Apr 16, 2009• 50 citations
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Abstract

A quantum pattern recognition scheme is presented, which combines the idea of a classic Hopfield neural network with adiabatic quantum computation. Both the input and the memorized patterns are represented by means of the problem Hamiltonian. In contrast to classic neural networks, the algorithm can return a quantum superposition of multiple recognized patterns. A proof of principle for the algorithm for two qubits is provided using a liquid-state NMR quantum computer.

DOI
10.1103/physreva.79.042321

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A quantum pattern recognition scheme is presented, which combines the idea of a classic Hopfield neural network with adiabatic quantum computation. Both the input and the memorized patterns are represented by means of the problem Hamiltonian. In contrast to classic neural networks, the algorithm can return a quantum superposition of multiple recognized patterns. A proof of principle for the algorithm for two qubits is provided using a liquid-state NMR quantum computer.
Abstract Quantum computing is a new mode that follows the laws of quantum mechanics. It performs computational tasks based on the control of quantum units. From the view of computable problems, quantum computers can only solve the problems that traditional computers can solve, but considering the efficiency of computation, due to the existence of quantum superposition, some known quantum algorithms are exponentially faster than traditional general-purpose computers. In this article, we combine quantum computing with a classical neural network to design a quantum Hopfield network. Each neuron is initialized to a specified state and evolved into a steady state. The output result is one of patterns in a training set. We also present an application of this protocol in image recognition. The simulation results show that this network works in the quantum environment and the output images are correct, therefore the feasibility of this protocol is verified.
Adiabatic quantum computing is successfully used to solve discrete optimization problems. The classical Hopfield neural network can also be applied to such problems but is primarily used for pattern recognition and reconstruction. Since its dynamics are deterministic, this can adversely affect its performance: the network sometimes gets trapped in local energy minima. This paper proposes a novel approach in which the Hopfield neural network learning rule (Hebbian rule) is combined with forward and reverse quantum annealing. This enables the use of adiabatic quantum annealers for pattern recognition, providing an alternative to traditional approaches.
There is increasing interest in quantum computing, because of its enormous computing potential. A small number of powerful quantum algorithms have been proposed to date; however, the development of new quantum algorithms for practical use remains essential. Parallel computing with a neural network has successfully realized certain unique functions such as learning and recognition; therefore, the introduction of certain neural computing techniques into quantum computing to enlarge the quantum computing application field is worthwhile. In this paper, a novel quantum associative memory (QuAM) is proposed, which is achieved with a quantum neural network by employing adiabatic Hamiltonian evolution. The memorization and retrieval procedures are inspired by the concept of associative memory realized with an artificial neural network. To study the detailed dynamics of our QuAM, we examine two types of Hamiltonians for pattern memorization. The first is a Hamiltonian having diagonal elements, which is known as an Ising Hamiltonian and which is similar to the cost function of a Hopfield network. The second is a Hamiltonian having non-diagonal elements, which is known as a neuro-inspired Hamiltonian and which is based on interactions between qubits. Numerical simulations indicate that the proposed methods for pattern memorization and retrieval work well with both types of Hamiltonians. Further, both Hamiltonians yield almost identical performance, although their retrieval properties differ. The QuAM exhibits new and unique features, such as a large memory capacity, which differs from a conventional neural associative memory.
This paper investigates the application of quantum neural networks (QNNs) for pattern recognition. Traditional neural networks face limitations in processing complex data due to their reliance on classical computing principles. QNNs leverage quantum mechanics phenomena, specifically superposition and entanglement, to potentially overcome these limitations. This research proposes a framework for constructing a QNN-based pattern recognition system. The core claim is to enhance pattern recognition accuracy and efficiency by utilizing these quantum properties. We detail the conversion process from classical neural networks to QNNs, highlighting the computational advantages offered by quantum computing. This work contributes to the nascent field of quantum machine learning, exploring the potential of QNNs to revolutionize pattern recognition tasks. The theoretical foundation presented here forms a basis for future research and development in this area.
By exploiting the properties of superposition and entanglement found in quantum systems Quantum Computation has been applied to the design of algorithms considerably more efficient than the known classical ones. Known examples are the Shor's factoring algorithm and the Grover's search algorithm. This paper investigates the possibility of employing Quantum Computing techniques to the design of learning algorithms for neural networks tasks such as pattern recognition. We propose a quantum learning algorithm for neural networks where all patterns of the training set are presented concurrently in superposition. In the process we propose a novel model of a quantum weightless neural node. The algorithm is a combination of a quantum search algorithm, a probabilistic quantum memory and a quantum neural network.